The Impact of Stochastic Noisy Feedback on Distributed Network Utility Maximization

—The implementation of distributed network utility maximization (NUM) algorithms hinges heavily on information feedback through message passing among network elements. In practical systems the feedback is often obtained using error-prone measurement mechanisms and suffers from random errors. In this paper, we investigate the impact of noisy feedback on distributed NUM. We first study the distributed NUM algorithms based on the Lagrangian dual method, and focus on the primal-dual (P-D) algorithm, which is a single time-scale algorithm in the sense that the primal and dual parameters are updated simultaneously. Assuming strong duality, we study both cases when the stochastic gradients are unbiased or biased, and develop a general theory on the stochastic stability of the P-D algorithms in the presence of noisy feedback. When the gradient estimators are unbiased, we establish, via a combination of tools in Martingale theory and convex analysis, that the iterates generated by distribute...

• Type: Conference
• Year: 2007
• Where: INFOCOM
• Authors: Junshan Zhang, Dong Zheng, Mung Chiang
• Keywords: Algorithm, Communications, INFOCOM 2007, Noisy Feedback, P-D Algorithms